Title

Best Possible Results in a Class of Inequalities, II

Abstract

We give a sufficient condition on a lower triangular infinite matrix A with nonnegative entries, and a positive sequence b = (bn), for an inequality of the form ||A(b|x|)||p ≤ K||x||p, x ∈ ℓp, to be best possible, in the sense that there is no positive sequence d = (dn) such that (dnb-1n) is a monotone unbounded sequence, and an inequality of the form above holds with b replaced by d. This condition permits easy proofs of "best possible" theorems that generalize a previous result concerning Hardy’s inequality. © 1994 Academic Press, Inc.

Publication Date

12-15-1994

Publication Title

Journal of Mathematical Analysis and Applications

Volume

188

Issue

3

Number of Pages

752-758

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1006/jmaa.1994.1460

Socpus ID

43949159543 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/43949159543

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